Lost soul, It's my opinion that what your thinking of doing is pretty stupid. No matter how trained a person is ( lets say you had all of Batmans skills, which you don't) you would still get caught by the police or killed by some mugger. Yeah Batfans If Batman was real he wouldn't survive long...sorry.
Even so, its not my place to tell you what to do and if your actually considering this, I admire your courage. I could see myself trying this one day in the future As a last resort in life....I really can see myself one day thinking *This world is such an auwful place, people hate eachother far too much. So I'm going to dedicate the rest of my time here in helping people who can't help themselves* Maybe that's how you feel right now? Anyway here's some advice if your going to do it.
If you live in a big city, wear a bullet proof vest that can take pistol rounds comfortably. If you live in America and a large city like New York, this is a must. You might also want to think about protecting other areas of your body like your crotch, legs and back. But don't wear anything that's too heavy or anything that limits your movement or speed too much.
You have 3 years martial arts training , that's a lot more than I have. But its not really enough. You should take an extended vacation to the far east and learn something more real. For urban combat you'll need to be skilled in blocking nife attacks, and short range gun blocking movements.
LEARN ABOUT HUMAN PSYCHOLOGY Read a lot of books on the stuff, take classes whatever. If you do this you'll be able to read situations a lot better and maybe even talk your enemy out of combat without violence.
This next bit is tuff on anyone, don't have too many personal ties. And do NOT EVER TELL ANYONE WHAT YOUR DOING. (this isn't a movie, nobody can keep this big a secret in real life.) The less people you know personally, the less you'll be worrying about them.
Basic detective skills and really just a bit of common sense are a must. Wear gloves at all times so to not leave finger prints everywhere, and wear boots with no tread.
I don't really think a costume would be very practicle if you ask me, but you'll definetly need a mask of some kind when your doing it, because you don't want anyone ID'n you to the police. Don't speak when your patrolling ( that sounds so buffy-like, damn that show for ruining a great word) If you speak someone may recognise your voice and ID you to the police, If you MUST SPEAK, use a fake voice in a different accent to your own, practise makes perfect btw.
Speed will be very important to you if you do this. Practise your running, because there will be situations where you need to high tail it outa there as fast as you can. But don't worry, most muggers are burger eating slocoaches.
Learn about the police in your town/city, learn police patrolling routes/times names of officers, what they look like and memorize them. I don't know how your going to get all that information but be creative about it and be descreet.
Weapons, well that's if you want them. personally I wouldn't use any, but thats because I'd never intend on killing anyone. Maybe some shuriken/shaken and a knife of some sort. If you want to be like the Punisher with guns then go ahead but I wouldn't advise it.
Well that's everything I can think of right now, but as Agent Smith would say, It is innevitable that you will get caught/shot/stabbed/die. So this is very much a last resort way of life.